Fluid Power Formula. These Formula Cover All Fluid Power Applications In This Manual

Transcription

1 These Formula Cover All Fluid Power Applications In This Manual For Computer Programs To Work Problems By Simply Filling In The Blanks See Your Local Fluid Power Distributor Many Companies Web Site Or CD Also See The Fluid Power Data Book Packaged With This Manual For Charts and Other Fluid Power Information

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3 Miscellaneous Fluid Power Formula Fluid Pressure= Force (Pounds) Unit Area (in 2 ) Velocity Through Pipes in Feet/Second (FPS)= x GPM (Flow Through Conduit) Internal Area of Conduit (in 2 ) Extra Hydraulic Oil Required to Fill a Volume (in 3 )= PSI x Volume (in 3 ) 250,000 Based on ½ of 1%/1,000 PSI Compressibility of a Fluid= 1 Bulk Modulus of the Fluid Specific Gravity of a Fluid= Weight of 1 ft 3 of the Fluid Weight of 1 ft 3 of Water Orifice Flow Pressure Drop ( P) Across an Orifice= (Flow in GPM (Q) x S G ) 2 C d = Orifice Coefficient x d 2 x P From According to Orifice Length and Shape is a Nominal Figure Flow GPM (Q) Across an Orifice= x C d x d 2 P S G S G = Specific Gravity Range For Hyd. Oil Diameter of an Orifice d 2 = Flow in GPM (Q) x S G.88 is a Nominal Figure x C d x P Circle Formula: Circumference of a Circle= πd 2 ( x Diameter Squared) Area of a Circle (in 2 )= π r 2 ( x radius 2 ) OR π D 2 OR.7854 D 2 4 Volume Formula: Volume (in 3 ) of Round Object= Area (in 2 ) x Length Volume of Square or Rectangular Object= Length x Width x Depth Tube Burst Calculations: Barlow Formula p = 2ST D 1 p= Burst Pressure PSI S= Ultimate Strength of Tube Material, PSI T= Nominal Wall Thickness, Inches D= Nominal OD of Tubing, Inches Boyles Law: PV 1 1 = PV 2 2 P 1 = Pressure 1 Absolute. (Gauge Pressure Plus 14.7) PV 2 2 P1 = V1 P 2 = Pressure 2 Absolute. (Gauge Pressure Plus 14.7) PV 1 1 P2 = V2 V 1 = Actual Gas Volume at Pressure 1 PV 2 2 V1 = P1 V 2 = Actual Gas Volume at Pressure 2 PV 1 1 V2 = P2

4 Miscellaneous Fluid Power Formula (Cont d. Charles Law: TV 1 2 = TV 2 1 T 1 = Absolute Temperature of Gas at Volume 1 (Temp. F ) TV 2 1 T1 = T 2 = Absolute Temperature of Gas at Volume 2 (Temp. F ) V2 V 1 = Volume of Gas at Temperature 1 TV 1 2 T2 = V 2 = Volume of Gas at Temperature 2 V1 TV 1 2 V1 = T2 TV 2 1 V2 = T1 General Gas Law: PV 1 1 PV 2 2 = P 1 = Pressure 1 Absolute. (Gauge Pressure Plus 14.7) T1 T2 P 2 = Pressure 2 Absolute. (Gauge Pressure Plus 14.7) PVT P1 = V 1 = Actual Gas Volume at Pressure 1 TV 2 1 V 2 = Actual Gas Volume at Pressure 2 PVT P2 = T 1 = Absolute Temperature of Gas at Volume 1(Temp. F ) TV 1 2 T 2 = Absolute Temperature of Gas at Volume 2(Temp. F ) PVT V1 = TP 2 1 PVT V2 = TP 1 2 PV 2 2 T1 = PVT PV 1 1 T2 = PVT Flow Velocity In Hydraulic Lines: Suction Line Low Pressure 2-4 Feet/Second Return Lines Low Pressure Feet/Second Medium Pressure Lines 500-3,000 PSI Feet/Second High Pressure Lines 3,000 PSI up Feet/Second Air-Oil Systems All Pressures 2-4 Feet/Second Work (in-lbs)= Force (Pounds) x Distance (Inches) (Feet) (ft-lbs) (Inches) gives Inch Pounds (Feet) gives Foot Pounds 2

5 Cylinder Formula Cylinder Force: Cap End Area (A) = Bore Diameter Squared x (0.7854D 2 ) Net Rod End Area = Bore Diameter Squared x Minus Rod Diameter Squared x ( D 2 Bore D 2 Rod) Force Extend = Cap End Area x PSI Force Extend Regeneration = Rod Area x PSI Force Retract = Net Rod End Area x PSI Note: Always size an air cylinder at least 25% above load balance or work force to get nominal speed and/or nominal force buildup time. For fast speed and fast work force buildup time size them up to 100% above load balance. (More than 100% above load balance gives negligible added cylinder speed.) Size hydraulic cylinders at least 10% above load balance or work force to get full speed at full force and/or nominal force buildup time. Cylinder Speed: Gallons per Inch (GPI) = A (Area) 231 (in 3 /Gallon) Inches per Minute (IPM) = Stroke Length x 60 (Seconds) Stroke Time (Seconds) Inches per Second (IPS) = Stroke Length Stroke Time (Seconds) Flow at Speed GPM = GPI x IPM IPM = GPM/GPI GPI = GPM/IPM Also: GPM = A (Area) x Stroke Length x 60 (Seconds) Stroke Time (Seconds) x 231 (in 3 /Gallon) A (Area) = Stroke Time (Seconds) x 231 (in 3 /Gallon) x GPM Stroke Length x 60 (Seconds Stroke Length = Stroke Time (Seconds) x 231 (in 3 /Gallon) x GPM A (Area) x 60 (Seconds) Stroke Time = A (Area) x Stroke Length x 60 (Seconds) GPM x 231 (in 3 /Gallon) Cylinder Rod End Intensification: Single Rod End Cylinders = Cylinder Bore A (Area) Cylinder Net Rod End A (Area) Double Rod End Cylinders = Net Rod End A (Area) of Large Rod Net Rod End A (Area) of Small Rod Cylinder Load Induced Pressure: Vertical Rod Down Cylinder = Load in Pounds Net Rod End A (Area) Vertical Rod Up Cylinder = Load in Pounds Bore A (Area) 3

6 Fluid Motor Formula Hydraulic Motors Torque, Horsepower, Speed Relations HP x 63,025 Torque (lb. in.)= For lb-ft use 5,252 Constant in Place of 63,025 2π Torque (lb. in.)= PSI x Displacement (in 3 /Revolution) 2 π Torque (lb. in.)= GPM x PSI x For more accurate answer use RPM in place of Torque (lb. in.)= Motor Displacement (in 3 /Revolution) Rule of Thumb: 1 CIR = 16 lb. 100 PSI Horsepower = Torque (lb-in) x RPM For Newton Meters Divide Answers 63,025 lb-in by RPM = Horsepower x 63,025 lb-ft. by Torque Flow Formula: Flow Rate at 100% Efficiency: Q (Flow GPM)= 3 RPM x CIR (in / Re volution Displacement) (in / Gallon) Multiply the answer by the manufacturers published efficiency percent for actual speed of a new motor. Efficiency Formula: Mechanical Efficiency Volumetric Efficiency Overall Efficiency Torque Actual E M= Torque Theoretical Q (Flow Actual) E M= Q (Flow Theoretical) HP Out E M= HP In Air Motors Design for maximum torque at approximately half operating air pressure. Follow manufacturers recommendations for a given motor type for Starting Torque, Maximum RPM, Maximum Torque and CFM air inlet flow. Run the air motor only when doing work. Remember an air motor can pull 7-15 compressor HP for each 1 HP output. 4

7 Flow Rate: Flow Rate at 100% Efficiency: Fluid Power Formula Hydraulic Pump Formula Q (Flow GPM)= 3 RPM x CIR (in / Re volution Displacement) (in / Gallon) Take Q times manufacturers Overall Efficiency Rating at a given pressure to get actual output. 3 3 Q (Flow GPM) x 231 (in / Gallon) Pump CIR (in / Re volution Displacement)= RPM Horsepower, Torque: Horsepower to drive a 100% efficiency HP = GPM x PSI x Horsepower to drive a 85% efficiency HP = GPM x PSI x Rule of Thumb: 1 1,500 PSI = 1 HP 3 PSI x CIR (in. / Re volutiondisplacement) Torque (lb. in.)= 2π HP x 63,025 Torque (lb. in.)= RPM Efficiency Formula for Pumps: Mechanical Efficiency Torque Actual E M= Torque Theoretical (Replace 2π with 24π for lb.ft.) (Replace 63,025 with 5,252 for lb.ft.) Volumetric Efficiency Q (Flow Actual) Ev= Q (Flow Theoretical) B 10 Bearing Life: HP Out Overall Efficiency E OA= HP In B 10 Bearing Life (Hours)=Rated Life (Hours) x Rated Speed (RPM) Rated Pr essure (PSI) x Actual Speed (RPM) Actual Pr essure(psi) Need to Remember Items About Pumps: Pumps do not make pressure they only make flow. Resistance to flow makes pressure. Fluid is pushed into a pumps inlet not sucked. A pump makes negative pressure at its inlet and Atmospheric pressure pushes fluid in to fill the void of low pressure. Where possible mount the pump so its inlet is below fluid level. Install a shutoff valve in the inlet line to reduce pump repair or replacement time. In most catalogs Gear and Vane pumps are rated at 1,200 RPM while Piston pumps are rated at 1,800 RPM. Multiply Gear and Vane pumps rated flow by 1.5 to get flow at 1,800 RPM. Multiply Piston pump flow by to get flow at 1,200 RPM. For fast priming of a pump in a closed center circuit use an Air Bleed Valve at its outlet. Pipe the return of the Air Bleed Valve so it terminates below fluid level. Always fill the case of a pressure compensated pump with hydraulic fluid before startup. Always pipe Case Drain Flow Lines to terminate below fluid level. When the Case Drain Line terminates above fluid level poor sealing of the Cylinder Block to the Valve Plate can suck in bypass fluid faster than it is made and empty the case of lubricating fluid. 5

8 Thermal Formulas Heat in a Hydraulic System Generated by Wasted Energy: Heat (BTU/Hour)=Flow Rate (GPM) x Pressure Drop (PSI) Heat (BTU/Hour) Flow Rate (GPM)= x Pressure Drop (PSI) Heat (BTU/Hour) Pr essure Drop (PSI)= Flow Rate (GPM x 1.485) Kilowatts Required to Heat Hydraulic Oil: Tank Capacity Gallons x (Desired Min. Fluid Temp. F- Min. Ambient Temp. F) KW = 800 x Allowable Time in Hours Note: Allow at least one hour and up to three hours for heating from minimum temperature. To only maintain heat, reduce the KW rating by 1/2 2/3 rds in relation to the time in hours allotted. Cooling Capacity of a Hydraulic Reservoir at the Poorest Ambient Conditions: 2 HP =.001 x (Max. Allowable Fluid Temp. F-Max. Ambient Air Temp. F) x Area in Contact W/Fluid (ft ) Equivalents One Horsepower Equals: 1 Bar at Sea Level Equals 746 Watts PSI 42.4 BTU/Minute atmospheres 2,545 BTU/Hour 33.6 Ft. Water Column 550 Ft. Lbs/Second 41 Ft Oil Column 33,000 Ft. Lb./Minute 1 PSI Equals One U.S. Gallon Equals: H g Four Quarts, Eight Pints Water Column 128 Ounces (Liquid) Bar Ounces (Weight) Pounds 1 Hg Equals Liters PSI 231 Cubic Inches Ft. Water Column Imperial Gallons 1 Ft. Water Column Equals One Liter Equals U.S. Gallons PSI 1 Atmosphere at Sea Level Equals 1 Ft. Oil Column Equals Bar PSI H g PSI 760 mm H g Atmosphere Decreases Approximately ½ PSI/1,000 Feet of Elevation 6

9 Accumulator Formula General Rules for Sizing and Applying Accumulators: Use dry nitrogen to pre-charge an accumulator. Other gasses may have ample pressure but can be a safety or explosion hazard. Use a pre-charge pressure of 85-90% of minimum system pressure. This keeps some fluid in the accumulator at all times and keeps the bladder or piston from bottoming out during normal operation. When pre-charge pressure is less than 50-60% of maximum pressure use a piston type accumulator. Bladder type accumulators sustain fast bladder chafing damage below the 50% mark. Piston type accumulators have no problem with low pre-charge pressure as long as the piston is not forced to bottom out as the nitrogen is compressed. Use a bladder type accumulator for short, rapid high pressure pulses such as shock absorbing. A piston type accumulator in this application can have premature seal failure due to lack of lubrication. Use the greatest possible difference in maximum system pressure and minimum working pressure to reduce accumulator size and/or number. Check accumulator pre-charge pressure daily on a new installation or replacement for first week of operation. If pressure is holding, check weekly for three weeks and if pressure is holding check every three to six months. See Chapter 16 Page 16-5 for a simple non-invasive way to check pressure. Always provide a means of automatically and/or manually dumping stored energy in the accumulator when the system is shut down. Also apply warning signs indicating an accumulator is present and must be checked for stored fluid, at the operating station, control panel and the accumulator. Always use a check valve between the pump and accumulator inlet to stop back flow to the pump when the circuit is shut down. 7

10 Accumulator Formula (Cont d.) Supplementing Pump Flow: Solving for accumulator size in Gallons V1= Gallons Information Required: Minimum pressure required to satisfy circuit needs: P2= PSI Maximum pressure available or allowed: P3= PSI Required cycle time of actuator in seconds AC= Seconds Oil volume capacity to cycle the actuator in Cubic Inches VA= in 3 Dwell time in seconds when no actuators are moving AD= Seconds Normal system operating temperature in F T= Temp. F Solve for minimum flow rate (FR) from pump in Cubic Inches/Second Solve for minimum pump flow (Q) in Cubic Inches/Second Solve for total cubic inches of fluid from accumulator V x Solve for ratio of Minimum to Maximum pressure (a) 8 FR= VA AD + AC Q=.26 x FR V x = VA (3.85 x Q x AC) a= P3 P2 From Chart 1, page 10 select (n) using this formula for Average Pressure P2 + P3 and Normal System Operating Temperature from above. 2 Select a figure for (f) from the Charts on pages using (a) and (n) above Solve for (V1) Accumulator Volume in Gallons V1= (V x / 231).807 x f Pick out an accumulator or accumulators with an empty capacity equal to or greater than the answer for V1 above. Pre-charge with dry nitrogen at 85% of P2. Making up for System Leakage: Solving for accumulator size in in 3 V1 in 3 Information Required: Minimum pressure required to satisfy circuit needs (P2): Maximum pressure available or allowed (P3): Required cycle time of actuator in seconds (LR) Length in minutes accumulator must hold pressure (TM) Solve for: Solve for ratio of Minimum to Maximum pressure (a) P2= PSI P3= PSI LR= in 3 /Minute TM= Minutes a= P3 P2 Since this application is Isothermal, it is not necessary to the reference Charts on pages (f) is found by f = 1 1 a Volume of oil required from accumulator (V x ) V x = LR x TM Solve for Accumulator Volume in in 3 (V1) V1= V x.807 x f Pick out an accumulator or accumulators with an empty capacity equal to or greater than the answer for V1 above. Pre-charge with dry nitrogen at 85% of P2.

11 Accumulator Formula (Cont d.) Emergency Power Supply: Solving for accumulator size in Gallons V1= Gallons Information Required: Minimum pressure required to satisfy circuit needs: P2= PSI Maximum pressure available or allowed: P3= PSI Oil volume capacity to cycle the actuators in in 3 VA= in 3 Normal system operating temperature in F T= Temp. F Solve for ratio of Minimum to Maximum pressure (a) a= P3 P2 From Chart 1, page 10 select (n) using this formula for Average Pressure P2 + P3 and Normal System Operating Temperature from above. 2 Select a figure for (f) from the Charts on pages using (a) and (n) above Solve for (V1) Accumulator Volume in Gallons V1= (VA / 231).807 x f Pick out an accumulator or accumulators with an empty capacity equal to or greater than the answer for V1 above. Pre-charge with dry nitrogen at 85% of P2. Hydraulic Line Shock Control: Solving for accumulator size in in 3 V1= in 3 Information Required: Normal system operating pressure (P2): P2= PSI Length of pipe generating the shock measured in feet between the pump and valve. (L): L= Feet Internal area of pipe in 1n 2 (A) A= in 2 Flow rate of pump in GPM (Q) Q= GPM Normal system operating temperature in F T= Temp. F From Chart 1, page 10 select (n) using P2 for Average Pressure and Normal System Operating Temperature from above. n= Solve for total volume in pipe (TV) in ft 3 TV= L x A 144 Solve for total weight of fluid in pipe in pounds (TW) TW= TV x Solve for fluid velocity in feet/second (FPS) (FV) FV=.3208 x Q A Pick a figure from Chart 2 page 10 for (C3) C3= Solve for V1 Accumulator volume in in 3 V1= FV 2 x TW x (n-1) x.186 P2 x C3 Pick out an accumulator or accumulators with an empty capacity equal to or greater than the answer for V1 above. Pre-charge with dry nitrogen at % of P2 9

12 Accumulator Formula (Cont d.) Piston Pump Discharge Shock Control: Solving for accumulator size in in 3 V1= in 3 Information Required: Normal system operating pressure (P2): P2= PSI Length of piston stroke in inches.(l): L= Inches Area of piston bores in the pump in in 2 (A) A= in 2 Pump constant (K) K=.60 for single piston single acting pumps..25 for single piston double acting pumps.25 for double piston single acting pumps..15 for double piston double acting pumps..13 for triple piston single acting pumps..06 for triple piston double acting pumps. Normal system operating temperature in F T= Temp. F From Chart 1, below, select (n) using P2 for Average Pressure and Normal System Operating Temperature from above. n= Pick a figure from Chart 2 below for (C1) Pick a figure from Chart 2 below for (C2) 10 C1= C2= Solve for V1 Accumulator volume in in 3 V1= L x A x K x C1 1- C2 Pick out an accumulator or accumulators with an empty capacity equal to or greater than the answer for V1 above. Pre-charge with dry nitrogen at % of P2 Chart 1 Chart 2 Average Temperature n c1 c2 c3 Pressure 77 F 108 F 140 F 171 F 200 F 220 F 1.41 Thru Thru Thru Thru Thru Thru Thru Thru Thru Thru Thru

13 To use this chart locate a in the left hand column and n across the top. The correct value for f is in the body of the chart where a and n intersect. When the exact value for a is not shown use the next higher figure. n a Continued on Next Page

14 To use this chart locate a in the left hand column and n across the top. The correct value for f is in the body of the chart where a and n intersect. When the exact value for a is not shown use the next higher figure. n a Continued on Next Page 12

15 To use this chart locate a in the left hand column and n across the top. The correct value for f is in the body of the chart where a and n intersect. When the exact value for a is not shown use the next higher figure. n a

16 SIZING A HYDRAULIC CIRCUIT THE FOLLOWING INFORMATION MUST BE KNOWN 1. Maximum force required Usually in pounds or tons of force 2. Total stroke required Usually in inches 3. High pressure stroke required Usually in inches 4. Total cylinder cycle time Usually in seconds 5. Maximum pressure allowed Arbitrarily decided by the engineer SAMPLE PROBLEM 1. Maximum force required 50,000 pounds 2. Total stroke required 42 inches 3. High pressure stroke required Total cylinder stroke 4. Total cylinder cycle time 10 seconds 5. Maximum pressure allowed 2,000 PSI A. Minimum Cylinder Bore = Maximum Force Re quired x 1.1 / Maximum PSI Allowed.7854 GPM = 50,000 Pounds x 1.1/2,000 PSI.7854 = diameter or a 6 Bore 2 PistonArea (in. ) x Stroke (Inches) x 60 Seconds Cycle Time (Seconds) x 231 (Cubic Inches/Gal.) x 84 x 60 GPM = = 61.7 GPM or a 65 GPM pump 10 x is for cylinder extend and retract. Rod displacement is disregarded in this example. C. Electric motor horse power = HP = GPM x PSI x HP = 65 x 2,000 x = or a 75 HP motor D. Tank size = 2-3 times pump GPM = 2 x 65 = 130 gallons = 150 gallon tank 3 x 65 = 195 gallons = 200 gallon tank 14

17 SIZING A HYDRAULIC CIRCUIT On the facing page is an exercise sizing a simple single cylinder hydraulic circuit with straight forward parameters. The example gives basic requirements for sizing a hydraulic cylinder powered machine. In the real world of circuit design, experience, knowing the process, the environment, the skill of the user, how long will the machine be in service, and other items affect cylinder and power unit choices. Before designing any circuit it is necessary to know several things. First is force requirement. Usually, the force to do the work is figured with a formula. In instances where there is no known mathematical way to figure force, use a mock up part on a shop press or on a prototype machine for best results. If all else fails, an educated guess may suffice. The sample problem requires a force of 50,000 pounds. Second, choose a total cylinder stroke. Stroke length is part of machine function and is necessary to figure pump size. Use a stroke of 42 inches in this problem. Third, how much of the stroke requires full tonnage? If only a small portion of the stroke needs full force, a HI-LO pump circuit and/or a regeneration circuit could reduce first cost and operating cost. This cylinder requires full tonnage for all 42 inches. Fourth, what is the total cylinder cycle time? Make sure the time used is for cycling the cylinder. Load, unload and dwell are part of the overall cycle time, but should not be included when figuring pump flow. Use a cylinder cycle time of 10 seconds for this problem. Finally, choose maximum system pressure. This is often a matter of preference of the circuit designer. Standard hydraulic components operate at 3000 PSI maximum, so choose a system pressure at or below this pressure. If a company has operating and maximum pressure specifications, adhere to them. Remember, lower working pressures require larger pumps and valves at high flow to get the desired speed. On the facing page part A, taking the square root of the maximum thrust, times 110%, for fast pressure buildup, divided by the maximum system PSI, divided by This gives a minimum cylinder bore of 5.244". Choose a standard 6" diameter cylinder for this system. To figure pump capacity, take the cylinder piston area in square inches, times the cylinder stroke in inches, times 60 seconds, divided by the cycle time in seconds, times 231 cubic inches per gallon. This shows a minimum pump flow of 61.7 GPM. A 65 GPM pump is the closest flow available. Never undersize the pump since this formula figures the cylinder is going maximum speed the whole stroke. The cylinder must accelerate and decelerate for smooth operation, so travel speed after acceleration and before deceleration should actually be higher than this formula allows. Figure horsepower by taking GPM times PSI times a constant of This comes out to HP, and is close to a standard 75 HP motor. This should be sufficient horsepower since the system pressure does not have to go to 2000 PSI with the cylinder size used. The tank size should be at least two to three times pump flow, which is three times sixty-five, or 195 gallons, so a 200 gallon tank is satisfactory. When using single acting cylinders or unusually large piston rods, size the tank for enough oil to satisfy cylinder volume without starving the pump. 15

18 SIZING A PNEUMATIC CIRCUIT THE FOLLOWING INFORMATION MUST BE KNOWN 1. Maximum force required Usually in pounds or tons of force 2. Total stroke required Usually in inches 3. Total cylinder cycle time Usually in seconds 4. System operating pressure Arbitrarily 80 PSI for most plants SAMPLE PROBLEM 1. Maximum force required 150 pounds 2. Total stroke required 14 inches 3. Total cylinder cycle time 4 seconds 4. System operating pressure 80 PSI A. Minimum Cylinder Bore = Maximum Force Re quired x 1.25 or 2 / Maximum PSI Allowed Pounds x 1.25/80 PSI.7854 = Diameter or a 2 Bore B. 3 V(Vol. in. ) x Compression Ratio (PSI /14.7) SCFM = Total Cycle Time ( Seconds ) x x x 28 x ( /14.7) SCFM = = 4.92 SCFM 4 x is for cylinder extend and retract. Rod displacement is disregarded in this example C. Min. Valve C v= Q T x S (Flow SCFM) (Abs.Temp.) (Spec.Gravity 1 for air) A g (Cons tan t) (Pr.Drop) (Outlet Pr.) (Atmos.Pr.) P x (P 2 + P A ) Min. Valve C v= x x ( ) =.161 = 1/8 ported valve 219# of thrust 2 80 PSI Load Cylinder will move at nominal speed 16

19 SIZING A PNEUMATIC CIRCUIT Sizing air cylinders is similar to sizing hydraulic cylinders. Most air systems operate around 100 to 120 PSI with approximately 80 PSI readily available at the machine site. This gives little or no option for selecting operating pressure. Since the compressor is part of plant facilities, the amount of cubic feet per minute (CFM) of air available for the air circuit usually is many times that required. It is good practice though, to check for ample CFM flow capabilities at the machine location. The only items needed to figure an air circuit is maximum force required, cylinder stroke, and cycle time. With this information, sizing cylinders, valves, and piping is simple. To figure the cylinder bore required, use the formula given at A. Notice the added multiplier on the force line. For an air cylinder to move at a nominal rate, it needs approximately 25% greater thrust than the force required to offset the load. When the cylinder must move fast, figure a force at up to twice that required to balance the load. The reason for this added force relates to filling an empty tank from a tank at 100 PSI. When air first starts transferring, a high pressure difference allows fast flow. As the two tanks get closer to the same pressure the rate of transfer slows until the gauges almost stop moving. The last five to ten PSI of transfer takes a long time. As the tanks get close to the same pressure, there is less reason for transfer since pressure difference is so low. If an air cylinder needs 78 PSI to balance the load, then it has only 2 PSI differential to move fluid into the cylinder at a system pressure of 80 PSI. If it moves at all, it is very slow and intermittent. As pressure differential increases, from higher inlet pressure or less load, the cylinder starts to move smoothly and steadily. The greater the differential the faster the cylinder movement. Once cylinder force is twice the load balance, speed increase is minimal. Using the 1.25 figure in the formula shows a cylinder bore of 1.72" minimum. Choose a 2" bore cylinder since it is the next size greater than To size the valve use the "flow coefficient," or C v rating formula. The C v factor is an expression of how many gallons of water pass through a valve, from inlet to outlet, at a certain pressure differential. There are many ways of reporting C v valve efficiency and some may be misleading. Always look at pressure drop allowed when figuring the C v, to be able to compare different brands intelligently. The formula shows a valve with 1/8" ports is big enough to cycle the 2" bore cylinder out 14" and back 14" in 4 seconds. There are many charts in data books as well as valve manufacturers catalogs that take the drudgery out of sizing valves and pipes. There are several computer programs as well to help in proper sizing of components. 17

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